2 Answers
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It should last years. If the reduction contains just vinegar, reduced until thick. This yields a very acidic solution very high in sugar (partly caramelized, depending on how long it was cooked). Other than sugar and acetic acid, there are some polyphenols and other gunk, some aromatics, and a bit of water.

There are two primary ways that food spoils: decay by microorganisms and oxidation. Decay happens when things get stinky and slimy, such as meat that has been left in a warm place for a few days. Bacteria can live in a lot of habitats, but need fairly mild conditions to thrive. Oxidation occurs when unsaturated fats (and other substances) pick up rogue chemicals from the environment, and is often refereed to as 'rancid'. This process will occur whenever something that can oxidize is exposed to air, but tends to progress slowly.

In the case of a balsamic reduction, the high acid and sugar content will stop bacterial growth. Since the reduction also contains acid, anything that could have been oxidized has already oxidized. Therefore a balsamic reduction should last pretty much forever. You might want to seal it up to keep bugs from getting in it, but other than that, it should be stable for years.

It tastes sweet, but it's still acidic as hell. On top of that, the reduction process is UHT pasteurization at its most basic. It'll last a long time in the refrigerator, three weeks or a month at least, as long as you didn't add anything weird to it.

Note: in my mind balsamic reduction is balsamic vinegar, reduced. No cornstarch no, sugar, no nothing. If you add stuff to it, that's definitely going to affect its shelf life.

I'm not planning on doing anything except reducing it. Should I store in the fridge or cabinet?
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yossarianAug 20 '10 at 15:05

@yossairan: Oh, refrigerate it certainly...I wouldn't leave it at room temp. It should keep as well or better than vinegrette.
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SatanicpuppyAug 20 '10 at 15:10

@yossarian Depends on your climate, but my local friendly supermarket sells it ready-reduced and we just store the bottle in the cupboard with no problems (it's sold as ambient goods)
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Rowland ShawAug 20 '10 at 16:06

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There's no need to refrigerate it...it's the same as your vinegar but in concentrated form.
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Darin SehnertAug 21 '10 at 0:56